Locally discontinuous but globally continuous Galerkin methods for elliptic problems

We propose and analyze a stabilized hybrid finite element method for elliptic problems consisting of locally discontinuous Galerkin problems in the primal variable coupled to a globally continuous problem in the multiplier. Numerical analysis shows that the proposed formulation preserves the main properties of the associate DG method such as consistency, stability, boundedness and optimal rates of convergence in the energy norm, and in the L2(Ω) norm for adjoint consistent formulations. For using an element based data structure, it has basically the same complexity and computational cost of classical conforming finite element methods. Convergence studies confirm the optimal rates of convergence predicted by the numerical analysis presented here, with accuracy equivalent or even better than the corresponding DG approximations.